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- Simple_Lie_group abstract "In group theory, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups.A simple Lie algebra is a non-abelian Lie algebra whose only ideals are 0 and itself. A direct sum of simple Lie algebras is called a semisimple Lie algebra.An equivalent definition of a simple Lie group follows from the Lie correspondence: a connected Lie group is simple if its Lie algebra is simple. An important technical point is thata simple Lie group may contain discrete normal subgroups, hence being a simple Lie group is different from being simple as an abstract group.Simple Lie groups include many classical Lie groups, which provide a group-theoretic underpinning for spherical geometry, projective geometry and related geometries in the sense of Felix Klein's Erlangen programme. It emerged in the course of classification of simple Lie groups that there exist also several exceptional possibilities not corresponding to any familiar geometry. These exceptional groups account for many special examples and configurations in other branches of mathematics, as well as contemporary theoretical physics.While the notion of a simple Lie group is satisfying from the axiomatic perspective, in applications of Lie theory, such as the theory of Riemannian symmetric spaces, somewhat more general notions of semisimple and reductive Lie groups proved to be even more useful. In particular, every connected compact Lie group is reductive, and the study of representations of general reductive groups is a major branch of representation theory.".
- Simple_Lie_group wikiPageID "292831".
- Simple_Lie_group wikiPageRevisionID "553474252".
- Simple_Lie_group hasPhotoCollection Simple_Lie_group.
- Simple_Lie_group subject Category:Lie_algebras.
- Simple_Lie_group subject Category:Lie_groups.
- Simple_Lie_group type Abstraction100002137.
- Simple_Lie_group type Algebra106012726.
- Simple_Lie_group type Cognition100023271.
- Simple_Lie_group type Content105809192.
- Simple_Lie_group type Discipline105996646.
- Simple_Lie_group type Group100031264.
- Simple_Lie_group type KnowledgeDomain105999266.
- Simple_Lie_group type LieAlgebras.
- Simple_Lie_group type LieGroups.
- Simple_Lie_group type Mathematics106000644.
- Simple_Lie_group type PsychologicalFeature100023100.
- Simple_Lie_group type PureMathematics106003682.
- Simple_Lie_group type Science105999797.
- Simple_Lie_group comment "In group theory, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups.A simple Lie algebra is a non-abelian Lie algebra whose only ideals are 0 and itself. A direct sum of simple Lie algebras is called a semisimple Lie algebra.An equivalent definition of a simple Lie group follows from the Lie correspondence: a connected Lie group is simple if its Lie algebra is simple.".
- Simple_Lie_group label "Enkelvoudige Lie-groep".
- Simple_Lie_group label "Simple Lie group".
- Simple_Lie_group label "Простая группа Ли".
- Simple_Lie_group label "單李群".
- Simple_Lie_group sameAs Enkelvoudige_Lie-groep.
- Simple_Lie_group sameAs m.01qtfb.
- Simple_Lie_group sameAs Q1003162.
- Simple_Lie_group sameAs Q1003162.
- Simple_Lie_group sameAs Simple_Lie_group.
- Simple_Lie_group wasDerivedFrom Simple_Lie_group?oldid=553474252.
- Simple_Lie_group isPrimaryTopicOf Simple_Lie_group.